The present invention relates to the field of phase to sinusoid amplitude conversion (PSAC) such as used in direct digital frequency synthesizers (DDFS) for converting phase data into amplitudes of a periodic function.
The synthesis of a desired frequency is a fundamental requirement in many fields, and specifically in modern frequency hopping wireless communications systems. In these types of systems, it is a key requirement to change the frequency of a reference oscillator very quickly and precisely while maintaining high spectral purity. DDFS systems are recognized as being best suited for such a purpose.
The basic principle of a DDFS involves the use of an accumulator to calculate phase angles around the unit circle. Sinusoid amplitudes corresponding to any such angle are obtained from a phase-to-sinusoid-amplitude converter. These samples can be passed to a digital-to-analog (DAC) converter then filtered by a low-pass filter. The output frequency is controlled by a frequency control word that is provided to the phase accumulator. The phase accumulator integrates the frequency control word every clock cycle and overflows through zero periodically resulting in a repeating ramp output.
The current design goal of DDFS architectures and techniques is to achieve a high level of spectral purity while reducing implementation costs and power consumption of the synthesizer. However, traditional architectures and techniques remain dependent on a look-up table and/or processing circuits that are complex, consume high power and require large integrated circuit space whether implemented as discrete components or as integrated single chip designs. These disadvantages pose particular difficulty for mobile wireless communication equipment where portable devices, to be practical, must be physically small with low battery drain yet must retain high spectral purity. Cellular telephones, military radios, satellite transponders or other modem transceivers are fundamentally designed to maximize the effective receive range, to capture and demodulate weak signals and minimize transmitted spurs and harmonics of the carrier. These design criteria are for the most part dependent on the spectral purity of the frequency generation components in the system.
Consequently, there is a need for phase to amplitude conversion for use in a DDFS, for example, that provides for a reduction in circuit complexity, a reduction in power consumption while maintaining a high level of spectral purity. More particularly, there is a need for a PSAC system and method that can imitate the behavior of a ROM based look up table by achieving good precision on the approximation of the sinusoid amplitude corresponding to all phase angles without a dependence on complex circuits that inherently use excessive power.
In accordance with one aspect of the present invention there is provided an apparatus (e.g., a PSAC) for determining an approximation of a sinusoidal amplitude for a given phase angle from a signal representing a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by: a lower horizontal-axis bound; a lower vertical-axis bound; and a slope represented as a sum of a plurality of slope elements, the apparatus comprising: a calculation mechanism receiving the signal for generating a set of outputs for each one of the plurality of linear line segments as a product of (i) a horizontal displacement representing a difference between the given phase angle and the lower horizontal-axis bound and (ii) each one of the plurality of slope elements; a selector mechanism for selecting (i) one of the set of outputs from the calculation mechanism and (ii) one of the lower vertical-axis bounds based on a selected one of the plurality of linear line segments; and an aggregation mechanism for evaluating the approximation of the sinusoidal amplitude as an aggregate of the selected one of the set of outputs from the selector mechanism and the one of the lower vertical-axis bounds.
In accordance with another aspect of the present invention there is provided, in a PSAC, a method of determining an approximation of a sinusoidal amplitude for a prescribed phase angle from a signal representing a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by: a lower horizontal-axis bound; a lower vertical-axis bound; and a slope represented as a sum of a plurality of slope elements, the method comprising: evaluating a set of values for each one of the plurality of linear line segments as a product of (i) a horizontal displacement representing a difference between the prescribed phase angle and the lower horizontal-axis bound and (ii) each one of the plurality of slope elements; and aggregating a selected set of values and a selected one of the lower vertical-axis bounds for a selected linear line segment to form the approximation of the sinusoidal amplitude for the prescribed phase angle.
In accordance with another aspect of the present invention there is provided a computer readable medium having stored thereon computer-executable instructions for determining an approximation of a sinusoidal amplitude for a prescribed phase angle from a signal representing a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by: a lower horizontal-axis bound; a lower vertical-axis bound; and a slope represented as a sum of a plurality of slope elements, the computer-executable instructions comprising the steps for: step for evaluating a set of values for each one of the plurality of linear line segments as a product of (i) a horizontal displacement representing a difference between the prescribed phase angle and the lower horizontal-axis bound and (ii) each one of the plurality of slope elements; and step for aggregating a selected set of values and a selected one of the lower vertical-axis bounds for a selected linear line segment to form the approximation of the sinusoidal amplitude for the prescribed phase angle.
In accordance with another aspect of the present invention there is provided an apparatus (e.g., a DDFS) comprising: means for generating a signal approximating a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by: a lower horizontal-axis bound; a lower vertical-axis bound; and a slope represented as a sum of a plurality of slope elements; generator means receiving the signal for generating a set of outputs for each one of the plurality of linear line segments as a product of a horizontal displacement representing a difference between the given phase angle and the lower horizontal-axis bound and each one of the plurality of slope elements; selector means for selecting one of the set of outputs from the generator means and one of the lower vertical-axis bounds based on a selected one of the plurality of linear line segments; means for evaluating an approximation of a sinusoidal amplitude as an aggregate of the selected one of the set of outputs from the selector mechanism and the one of the lower vertical-axis bounds; and means for converting the approximation of the sinusoidal amplitude from the adder means into an analog signal.
In accordance with another aspect of the present invention there is provided, in a DDFS, a method of determining an approximation of a sinusoidal amplitude for a prescribed phase angle, the method comprising: generating a signal approximating a quadrant of a sinusoid function defined by a plurality of linear line segments of substantially equal length, each linear line segment being defined by: a lower horizontal-axis bound; a lower vertical-axis bound; and a slope represented as a sum of a plurality of slope elements; generating a set of outputs for each one of the plurality of linear line segments as a product of a horizontal displacement representing a difference between the given phase angle and the lower horizontal-axis bound and each one of the plurality of slope elements; selecting one of the set of outputs generated and one of the lower vertical-axis bounds based on a selected one of the plurality of linear line segments; and evaluating an approximation of a sinusoidal amplitude as an aggregate of the selected one of the set of outputs and the one of the lower vertical-axis bounds; and converting the approximation of the sinusoidal amplitude into an analog waveform.